A thermodynamic phase transition is characterized by the non-analyticity of thermodynamic observables with respect to temperature across two or more different phases. These phase transitions were systematically classified by Ehrenfest [1]}, [2]}. Ehrenfest's classification is based on the order of the phase transition, i.e. a \(r\) th order phase transition is characterized by the \(r\) th derivative of the partition function (or free energy) becoming discontinuous at the temperature where the phase transition takes place. A thermodynamic function that takes different values across different phases is called an order parameter.
